Insertion and extraction of a message in an image

ABSTRACT

The invention concerns a method of inserting a message in an image, the message comprising binary symbols which are each referenced by an index, characterized in that it comprises, for a coefficient (Y n ) of the image, the steps of:
         determining (E 9 ) a watermarked value (Y′ n ) of the coefficient, according to the binary value (b) of a symbol of the message and according to the index (i) of the symbol,   inserting (E 11 ) the watermarked value in place of the value of the coefficient.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention concerns a method of inserting a message such as asecret watermark in a digital signal.

It also concerns a method of extracting a message inserted in a digitalsignal.

Correspondingly, the present invention concerns a device for inserting amessage and a device for extracting the message, adapted respectively toimplement the insertion and extraction methods according to theinvention.

2. Description of the Related Art

The digital signal considered hereinafter will more particularly be adigital image signal.

The message insertion envisaged in the context of the invention lies inthe technical field of watermarking digital data, which can beinterpreted as the insertion of a watermark in the digital data makingit possible for example to authenticate the content of a digital datafile. This watermarking is also referred to as digital tattooing.

Watermarking in general terms comprises the modification of coefficientsrepresenting the digital image. This modification is imperceptible tothe eye but can be decoded by an appropriate decoder.

The concern here is with the robust insertion of a message.

The insertion of a message is said to be robust if the message cansubsequently be extracted even if the image has undergone geometricdistortions such as dividing part of the image, a change of scale or arotation.

In order to obtain such robustness, solutions have been proposed.

The document “Data Hiding for Video-in-Video” by M. D. Swanson, B. Zhuand A. H. Tewfik, which appeared in International Conference on ImageProcessing, 1997, p. 676-679, proposes a method of inserting a messagein an image according to which an image is divided into blocks and theneach of these blocks is transformed according to a transformation of theDCT type (from the English Discrete Cosine Transform).

The coefficients of the transformed blocks are then modified so that theprojection of these blocks onto pseudo-random sequences is quantizedaccording to one of two values, chosen according to the value of thebinary symbol which it is wished to insert in the block.

This method is not robust to geometric distortions since the divisioninto blocks cannot be reproduced after geometric distortion.

The document “Preprocessed and Postprocessed Quantization IndexModulation Methods for Digital Watermarking” by B. Chen and G. W.Wornell, which appeared in Security and Watermarking of MultimediaContent (E100), San Jose, January 2000, and the document “ProvablyRobust Digital Watermarking” which appeared in Proc. of SPIE: MultimediaSystems and Applications II, Vol. 3845, by the same authors, present amessage insertion in an image according to which binary values areinserted by scalar or vector quantization of one or more pixels of theimage.

For example, if scalar quantization is used, the pixel is modified intoits quantized value by a first quantizer if the value to be inserted iszero or by a second quantizer if the value to be inserted is one.

The extraction is carried out by identification of the quantizer usedfor each pixel.

This method is not robust to geometric distortions. This is because,according to this method, the bits to be inserted are associated withthe pixels of the image according to a predefined division. In the eventof geometric distortion between insertion and extraction, it is nolonger possible to find this division. Consequently the associationbetween pixel and message bit can no longer be made and extractionbecomes impossible.

SUMMARY OF THE INVENTION

The present invention aims to remedy the drawbacks of the prior art byproviding a method and a device for inserting a message in a digitalimage which is robust to geometric transformations such as division,change of scale or rotation.

To this end, the invention proposes a method of inserting a message inan image, the message comprising binary symbols which are eachreferenced by an index, characterized in that it comprises, for acoefficient of the image, the steps of:

-   -   determining a watermarked value of the coefficient, according to        the binary value of a symbol of the message and according to the        index of the symbol,    -   inserting the watermarked value in place of the value of the        coefficient.

The invention makes it possible to carry out a message insertion in animage which is robust to geometric transformations such as division,change of scale or rotation. This is because a pixel of the image ismodified according to the value of a binary symbol to be inserted andaccording to the index of this binary symbol in the message. Themodified value of the pixel carries these two items of information whichallow subsequent extraction of the inserted symbol, even in the case ofgeometric distortion.

According to a preferred characteristic, the watermarked value isselected from a range of given values determined around the value of thecoefficient according to a psycho-visual model.

Thus the modification of the pixels remains invisible.

According to a preferred characteristic, the determination of awatermarked value of the coefficient comprises:

-   -   selecting a modified value of the coefficient,    -   determining a symbol index, according to the modified value and        a first predetermined function,    -   determining the value of the message symbol corresponding to the        predetermined index,    -   verifying that the value of the symbol previously determined        corresponds to the transformation of the modified value by a        second predetermined function.

This makes it possible to ensure that the modified value of the pixelrelates both to the information on the value of the binary symbol andits index in the message.

According to a preferred characteristic, if the value of the symbolpreviously determined corresponds to the transformation of the modifiedvalue by a second predetermined function, the method comprises the stepof:

-   -   testing for determining whether the number of times the symbol        has already been inserted in a coefficient of the image is the        lowest amongst all the symbols whose index was determined        according to the modified value and the first predetermined        function and whose value corresponds to the transformation of        the modified value by the second predetermined function, for the        coefficient in question.

Thus it is the symbol which has least often been inserted in the imagewhich will be chosen. Overall, the method tends to insert each symbol ofthe message the same number of times in the image.

According to a preferred characteristic, the insertion of the binarysymbols is carried out on the luminance value of the pixels of theimage. This gives good experimental results.

According to an alternative embodiment, the index of the symbol isautomatically determined in accordance with the coefficient.

The invention also relates to a method of extracting a message from animage, the message having been inserted by the method presented above,characterized in that it comprises the steps of:

-   -   calculating a symbol index and a binary value according to the        watermarked value of the coefficient, for each coefficient of        the image,    -   totaling the number of each of the binary values obtained for        each of the symbols,    -   allocating to each symbol the binary value having the largest        total.

According to a preferred characteristic, the symbol index for acoefficient is determined according to the watermarked value of thecoefficient and the first predetermined function.

According to a preferred characteristic, the binary value of the symbolfor a coefficient is determined according to the watermarked value ofthe coefficient and the second predetermined function.

According to a further embodiment, the method of extracting a messagefrom an image, the message having been inserted by the method presentedabove, is characterized in that it comprises the steps of:

-   -   calculating a symbol index according to the watermarked value of        the coefficient, for each coefficient of the image,    -   calculating a first and a second value according to the        watermarked value, for each coefficient of the image,    -   first totaling of the absolute values of the differences between        the watermarked value and the first value, for each symbol,    -   second totaling of the absolute values of the differences        between the watermarked value and the second value, for each        symbol,    -   allocating to each symbol a binary value according to the        smallest total amongst the first and second totals.

Correspondingly, the invention concerns a device for inserting a messagein an image, the message containing binary symbols which are eachreferenced by an index, characterized in that it comprises:

-   -   means of determining a watermarked value of a coefficient of the        image, according to the binary value of a symbol of the message        and according to the index of the symbol,    -   means of inserting the watermarked value in place of the value        of the coefficient.

The insertion device according to the invention comprises means ofimplementing the characteristics disclosed above.

The invention also concerns an extraction device comprising means ofimplementing the characteristics presented above.

The insertion device and the extraction method and device haveadvantages similar to those presented above.

The invention also concerns a digital apparatus including the deviceaccording to the invention or means of implementing the method accordingto the invention. This digital apparatus is for example a digitalcamera, a digital camcorder, a scanner, a printer, a photocopier or afacsimile machine. The advantages of the device and of the digitalapparatus are identical to those disclosed above.

An information storage means which can be read by a computer or by amicroprocessor, optionally integrated into the device, and optionallyremovable, stores a program implementing the method according to theinvention.

A computer program which can be read by a microprocessor and containingone or more sequences of instructions is able to implement the methodsaccording to the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The characteristics and advantages of the present invention will becomemore clear from a description of a preferred embodiment illustrated bythe accompanying drawings, in which:

FIG. 1 is an embodiment of a device implementing the invention,

FIG. 2 depicts a device for inserting a message in an image, accordingto the invention, and a corresponding extraction device,

FIG. 3 depicts an embodiment of a method of inserting a message in animage, according to the invention,

FIG. 4 depicts a first embodiment of a method of extracting a messagefrom an image, according to the invention,

FIG. 5 depicts a second embodiment of a method of extracting a messagefrom an image, according to the invention,

FIG. 6 illustrates an alternative embodiment of a method of inserting amessage in an image, according to the invention,

FIG. 7 is a flowchart of the method illustrated on FIG. 6.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

According to the chosen embodiment depicted in FIG. 1, a deviceimplementing the invention is for example a microcomputer 10 connectedto various peripherals, for example a digital camera 107 (or a scanner,or any image acquisition or storage means) connected to a graphics cardand supplying information to be processed according to the invention.

The device 10 comprises a communication interface 112 connected to anetwork 113 capable of transmitting digital data to be processed orconversely transmitting data processed by the device. The device 10 alsocomprises a storage means 108 such as for example a hard disk. It alsocomprises a drive 109 for a disk 110. This disk 110 can be a diskette, aCD-ROM or a DVD-ROM for example. The disk 110, like the disk 108, cancontain data processed according to the invention as well as the programor programs implementing the invention which, once read by the device10, will be stored on the hard disk 108. According to a variant, theprogram enabling the device to implement the invention can be stored inread only memory 102 (referred to as ROM in the drawing). In a secondvariant, the program can be received and stored in an identical fashionto that described above by means of the communication network 113.

The device 10 is connected to a microphone 111. The data to be processedaccording to the invention will in this case be the audio signal.

This same device has a screen 104 for displaying the data to beprocessed or serving as an interface with the user, who can thusparameterize certain processing modes by means of the keyboard 114 orany other means (a mouse for example).

The central unit 100 (referred to as CPU in the drawing) executes theinstructions relating to the implementation of the invention,instructions stored in the read only memory 102 or in the other storageelements. On powering up, the processing programs stored in anon-volatile memory, for example the ROM 102, are transferred into therandom access memory RAM 103, which will then contain the executablecode of the invention as well as registers for storing the variablesnecessary for implementing the invention.

In more general terms, an information storage means, which can be readby a computer or by a microprocessor, optionally integrated into thedevice, and optionally removable, stores a program implementing themethod according to the invention.

The communication bus 101 allows communication between the variouselements included in the microcomputer 10 or connected to it. Therepresentation of the bus 101 is not limiting and in particular thecentral unit 100 is able to communicate instructions to any element ofthe microcomputer 10 directly or by means of another element of themicrocomputer 10.

An embodiment of a device for inserting a message in an image accordingto the invention is described with reference to FIG. 2. The insertiondevice is integrated into an apparatus, which is for example a digitalcamera, a camcorder, a scanner, a printer, a photocopier, a facsimilemachine, a database management system or a computer.

The digital image IM is supplied by a source 1. The image IM consists ofa series of digital samples. An original image IM can be represented bya series of pixels coded for example in 8 bits or bytes. The black andwhite image IM can thus be decomposed in the spatial domain into a setof coefficients on 256 levels of gray, each coefficient valuerepresenting a pixel of the image IM.

The message M to be inserted is formed from alphanumeric characterswhich are converted into a binary code. This binary code is stored in amemory 3.

In general terms, an insertion device 2 can be assimilated to a coderwhich codes a message in an image IM. A watermarked image I′ is suppliedat the output of the coder 2.

The insertion device according to the invention comprises:

-   -   means 21 of determining a watermarked value Y′_(n) of a        coefficient of the image, according to the binary value of a        symbol of the message and according to the index of the symbol,    -   means 22 of inserting the watermarked value in place of the        value of the coefficient.

The functioning of the insertion device will be detailed below.

The image I′ can undergo various processing steps, such as compressionand decompression or geometric distortions: division, change of scale orrotation for example. These processing steps are carried out by a device4. The result is an image I″.

The image I″ is supplied to a decoder 5, which carries out theextraction of the message M.

The extraction device according to the invention comprises:

-   -   means 51 of calculating a symbol index and a binary value        according to the watermarked value of the coefficient, for each        coefficient of the image,    -   means 51 of totaling the number of each of the binary values        obtained for each of the symbols,    -   means 52 of allocating to each symbol the binary value having        the highest total.

The functioning of the extraction device will be detailed below.

FIG. 3 depicts an embodiment of a method of inserting a message in animage IM, according to the invention. This method is implemented in thecoding device and comprises steps E1 to E12.

The method is implemented in the form of an algorithm which can bestored in whole or in part in any information storage means capable ofcooperating with the microprocessor. This storage means can be read by acomputer or by a microprocessor. This storage means is optionallyintegrated into the device, and may be removable. For example, it maycomprise a magnetic tape, a diskette or a CD-ROM (fixed-memory compactdisk).

Step E1 is an initialization at which a table OC containing as manyvalues as there are bits in the message M to be inserted in the image IMis cleared, i.e. that every element OC_(i) of the table OC is nullified.A value OC_(i) of the table OC indicates the number of times the bitB_(i) of the message has been inserted in a coefficient of the image.

The following step E2 is the calculation of a psycho-visual model MV onthe image IM. The psycho-visual model MV represents in each pixel of theimage the maximum modification value acceptable on the value of thepixel without this being perceptible. In English, the term “JustNoticeable Difference” (JND) is used.

This calculation is conventional. For example, the article “APerceptually Tuned Subband Image Coder Based on the Measure of JustNoticeable Distortion Profile”, by C. H. Chou and Y. C. Li, in IEEETrans. on Circuits and Systems for Video Technology, 5(6): 467-476,1995, describes such a method.

The result of the psycho-visual model is a maximum distortion ε_(n) atany pixel P_(n) of the image.

The following step E3 is the selection of a pixel P_(n) of the image.Hereinafter, the pixels are processed one by one, and are selectedeither in a random order or in a predetermined order, for example fromleft to right and from top to bottom.

In the preferred embodiment, the binary message symbols are inserted onthe luminance components of the pixels. If the image is expressed bycolor components, it is first converted into luminance and chrominancecomponents. In a variant, the insertion can be carried out on the colorcomponents.

Hereinafter, the luminance component Y_(n) of each pixel P_(n) of theimage is considered.

At the following step E4, a variable IND_(n) is initialized to the value−1. The variable IND_(n) is associated with the current pixel P_(n). Awatermarked luminance value Y′_(n) for the current pixel is initializedto the value Y_(n).

At the following step E5, a luminance variable Y is initialized to thevalue Y_(n)−ε_(n). For the current pixel P_(n), the luminance variable Ywill hereinafter take all the values between (Y_(n)−ε_(n)) and(Y_(n)+ε_(n)) in steps of one unit.

The following step E6 is first of all the determination of a bit index ito be inserted on the current luminance Y_(n). This determination ismade according to the current luminance variable Y: i=f₁(Y).

The index i of the bit to be inserted is determined in the followingmanner:

The remainder of the integer division of the current luminance Y by aninteger multiple α of the length of the message is calculated. The indexi is equal to the result of the integer division of this calculation bythe same multiple α. The integer α represents one step.

For example, if the length of the message to be inserted is 32 bits andthe integer α is equal to four, the following results are obtained:

For Y∈[0, 4[, i=0,

For Y∈[4, 8[, i=1,

For Y∈[8, 12[, i=2,

. . .

For Y∈[124, 128[, i=31,

For Y∈[128, 132[, i=0,

. . .

At step E6, the binary value b of the bit of index i is also extractedfrom the message.

Step E6 also comprises the determination of a second binary value b′ asa function of the current luminance variable Y: b′=f₂(Y).

The binary value b′ is determined in the following manner:

b′=1 if the remainder of the integer division of Y by the value α isstrictly less than α/2,

b′=0 if the remainder of the integer division of Y by the value a isgreater than or equal to α/2.

Thus, if the value α is equal to four:

b′=1 for Y in the intervals [0, 2[, [4, 6[, [8, 10[ . . . , and

b′=0 for Y in the intervals [2, 4[, [6, 8[, [10, 12[ . . . .

The following step E7 is a test for determining whether the binaryvalues b and b′ determined at the previous step are equal.

If the response is negative, this means that the current luminance valueY determined at step E5 is not an acceptable watermarked value. In thiscase, step E7 is followed by step E10 at which the current luminancevalue Y is incremented by one unit as long as the limit value(Y_(n)+ε_(n)) has not been reached.

Step E10 is followed by the previously described step E6. When at theend of step E10 all the luminance values have been tested between(Y_(n)−ε_(n)) and (Y_(n)+ε_(n)), this step is followed by step E11,which is described below.

When the response is positive to step E7, this means that the currentluminance value Y is an acceptable watermarked value. In this case, stepE7 is followed by step E8, which is a test for determining whether thenumber of times OC_(i) that the bit B_(i) of the message has beeninserted in a coefficient of the image is strictly less than the numberof times the bit of index IND_(n) has been inserted in a coefficient ofthe image.

If the response is positive, this means that the bit of index idetermined at step E6 is the one which has been inserted least often inthe coefficients of the image, amongst the bits determined duringprevious passages through step E6 and satisfying the condition of stepE7, for the current pixel of the image.

When the value IND_(n) is equal to its initialization value −1, thismeans that the bit of index i determined at step E6 is the first bitsatisfying the condition of step E7 for the current pixel of the image.

In these two cases, step E8 is followed by step E9, at which the markedvalue Y′_(n) tor the current pixel P_(n) is set to the current value Yand the variable IND_(n) is set to the value i. Thus the bit B_(i) ofbinary value b and index i is not only able to be inserted on theluminance of the current pixel but is also the bit which has beeninserted least often amongst the bits insertable on the pixel inquestion. Thus the method seeks to insert all the bits of the messagethe same number of times. All the bits are inserted with the samerobustness.

As long as all the possible luminance values have not been consideredfor the current pixel P_(n), step E9 is followed by the previouslydescribed step E10 in order to consider a new luminance value for thecurrent pixel.

When all the possible luminance values have been considered for thecurrent pixel, then step E9 is followed by step E11.

At step E11, the luminance value Y_(n) is replaced by the watermarkedvalue Y′_(n) determined during the last passage through step E9. Inaddition, the number of times OC_(i) that the bit B_(i) of the messagehas been inserted in a coefficient of the image is incremented by oneunit, with here the parameter i equal to the value IND_(n) determinedduring the last passage through step E9.

In the case where IND_(n) is equal to −1 at the end of the processing ofthe pixel P_(n), this means that no bit of the message can be insertedin the luminance of this pixel. The watermarked value Y′_(n) remainsequal to its initialization value Y_(n). The number OC_(INDn) isincremented by one unit, but does not correspond to any bit of themessage.

As long as all the pixels of the image have not been processed, step E11is followed by step E12, at which a subsequent pixel is considered. StepE12 is followed by the previously described step E4.

When all the pixels of the image have been processed, then thewatermarking of the image is terminated.

FIG. 4 depicts a first embodiment of the extraction of a messagepreviously inserted in an image as previously disclosed.

This method is implemented in the extraction device and comprises stepsE20 to E25.

The method is implemented in the form of an algorithm which can bestored in whole or in part in any information storage means capable ofcooperating with the microprocessor. This storage means can be read by acomputer or by a microprocessor. This storage means is optionallyintegrated into the device, and may be removable. For example, it maycomprise a magnetic tape, a diskette or a CD-ROM (fixed-memory compactdisk).

Step E20 is an initialization at which two tables, each containing asmany values S_(0,i) and S_(1,i) as there are bits to be extracted, havetheir values all initialized to the value zero.

The following step E21 is the selection of a first pixel of the image.As with the insertion, the pixels are selected in a random order or in apredetermined order.

At the following step E22, a bit index i in the message and a bit valueb are calculated according to the luminance value Y_(n) of the currentpixel P_(n).

These calculations are identical to those carried out during step E6 ofthe insertion. In particular, the same functions f₁ and f₂ are used:i=f₁(Y_(n)) and b=f₂(Y_(n)).

If the value of the bit is zero, then the counter S_(0,i) is incrementedby one unit.

If the value of the bit is one, then the counter S_(1,i) is incrementedby one unit.

The following step E23 is a test for determining whether the currentpixel is the last pixel of the image to be processed. If the response isnegative, then this step is followed by step E24, at which a subsequentpixel is considered. Step E24 is followed by the previously describedstep E22.

When the response is positive at step E23, then the value of each bit ofthe message is determined at step E25.

For this purpose, the values S_(0,i) and S_(1,i) are compared for eachbit of index i. If S_(0,i) is greater than S_(1,i), then the bit ofindex i receives the value zero. Conversely, if S_(1,i) is greater thanS_(0,i), then the bit of index i receives the value one.

If the values S_(0,i) and S_(1,i) are zero, then the value of thecorresponding bit is indeterminate.

FIG. 5 depicts a second embodiment of the extraction of the message.

This embodiment is differentiated from the previous one by steps E22′and E25′, which replace respectively steps E22 and E25 of the previousembodiment. The other steps are unchanged.

At step E22′, the bit index i in the message is calculated according tothe luminance value Y_(n) of the current pixel P_(n), as during stepE22.

In addition, two values Y₁ and Y₂ are calculated in the followingmanner:

Y₁ is the value closest to Y_(n) satisfying equality:

Y₁=α.n₁+3.α/4, with n₁ any positive integer, and

Y₂ is the value closest to Y_(n) satisfying equality:

-   -   Y₂=α.n₂+α/4, with n₂ any positive integer.

The absolute value of the difference between the current luminance valueY_(n) and the value Y₁ is added to the sum S_(0,i).

Likewise, the absolute value of the difference between the currentluminance value Y_(n) and the value Y₂ is added to the sum S_(1,i).

At step E25′, the value of the bit B_(i) is zero if the sum S_(0,i) isstrictly less than the sum S_(1,i). The value of the bit B_(i) is one ifthe sum S_(1,i) is less than or equal to the sum S_(0,i).

If the values S_(0,i) and S_(1,i) are zero, then the value of thecorresponding bit is indeterminate.

FIG. 6 illustrates an alternative embodiment of an insertion methodaccording to the invention.

In this embodiment, the index of the symbol is automatically determinedin accordance with the luminance component Y_(n):i=f ₁(Y _(n))

A function f₁ of the same type as described above can be used. If themessage to be inserted is four-bit long as exemplified on FIG. 6, thefollowing results are obtained:

For Y_(n)∈[0, 4[, i=0,

For Y_(n)∈[4, 8[, i=1,

For Y_(n)∈[8, 12[, i=2,

For Y_(n)∈[12, 16[, i=3,

For Y_(n)∈[16, 20[, i=0,

. . .

The watermarked value Y′_(n) is then determined depending on the binaryvalue b of the message at index i (i.e. the value of bit i in themessage): b=message (i).

The watermarked value Y′_(n) is for instance determined such that Y_(n)and Y′_(n) remain within the same of the above intervals(|Y_(n)−Y′_(n)|<α, here |Y_(n)−Y′_(n)|<4) and Y′_(n) has a firstpredetermined value if b is null and a second predetermined value if bis not null.

For example, still referring to FIG. 6, if a value Y_(n)=17 in theoriginal image is input, a bit corresponding to index i=0 is embedded,as f1 (Y_(n)=17)=0.

The value Y′_(n) is set at 17 if bit 0 is null in the message (in caseb=message(0)=0) while the value Y′_(n) is set at 19 if bit 0 is not nullin the message (in case b=message (0)=1).

Similarly, if the value Y_(n) is 22, bit 1 in the message isautomatically embedded and the value Y′_(n) is then set at either 21 or23 (depending on the value of bit 1 in the message).

FIG. 7 provides a flowchart showing the process which has just beendescribed.

Naturally the present invention is in no way limited to the embodimentsdescribed and depicted, but on the contrary encompasses any variantwithin the capability of a person skilled in the art.

1. A method of inserting a message in an image, the message comprisingbinary symbols which are each referenced by an index, comprising, for acoefficient of the image, the steps of: determining a watermarked valueof the coefficient, according to the binary value of a symbol of themessage and according to the index of the symbol in the message, whereinthe index of the symbol is determined from a value of the coefficient ofthe image, and inserting the watermarked value in place of the value ofthe coefficient, wherein the determination of a watermarked value of thecoefficient comprises: selecting a modified value of the coefficient,determining a symbol index, according to the modified value and a firstpredetermined function, determining the value of the message symbolcorresponding to the determined symbol index, and verifying that thevalue of the message symbol previously determined corresponds to thetransformation of the modified value by a second predetermined function.2. An insertion method according to claim 1, wherein the watermarkedvalue is selected from a range of values determined around the value ofthe coefficient according to a psycho-visual model.
 3. An insertionmethod according to claim 1, wherein, if the value of the message symbolpreviously determined corresponds to the transformation of the modifiedvalue by a second predetermined function, the method comprises the stepof: testing for determining whether the number of times the symbol hasalready been inserted in a coefficient of the image is the lowestamongst all the symbols whose index was determined according to themodified value and the first predetermined function and whose valuecorresponds to the transformation of the modified value by the secondpredetermined function, for the coefficient in question.
 4. An insertionmethod according to claim 1, wherein the insertion of the binary symbolsis carried out on the value of the luminance of the pixels of the image.5. An insertion method according to claim 1, wherein said index of thesymbol is automatically determined in accordance with the coefficient ofthe image.
 6. An apparatus for processing a digital image, comprisingmeans adapted to implement the method according to claim
 1. 7. A methodof extracting a message from an image, comprising the steps of: for eachcoefficient of the image, calculating a symbol index and a binary value,both according to a value of the coefficient, totaling the number ofeach of the binary values obtained for each of the symbol indexes, andallocating to each symbol index the binary value having the largesttotal.
 8. An extraction method according to claim 7, wherein, for acoefficient of the image, the symbol index is determined according tothe watermarked value of the coefficient and a first predeterminedfunction.
 9. An extraction method according to claim 7, wherein, for acoefficient of the image, the binary value is determined according tothe value of the coefficient and a second predetermined function.
 10. Amethod of extracting a message from an image, comprising the steps of:for a coefficient of the image, calculating a symbol index according toa value of the coefficient, for each coefficient of the image,calculating a first and a second value, both according to a value of thecoefficient, for each coefficient of the image, first totaling of theabsolute values of the differences between the value of the coefficientand the first value, for each symbol index, and second totaling of theabsolute values of the differences between the value of the coefficientand the second value, for each symbol index, allocating to each symbolindex a binary value according to the smallest total amongst the firstand second totals.
 11. An extraction method according to claim 10,wherein, for a coefficient, the symbol index is determined according tothe value of the coefficient and a first predetermined function.
 12. Adevice for inserting a message in an image, the message containingbinary symbols which are each referenced by an index, comprising: meansfor determining a watermarked value of a coefficient of the image,according to the binary value of a symbol of the message and accordingto the index of the symbol, wherein the index of the symbol isdetermined from a value of the coefficient of the image, and means forinserting the watermarked value in place of the value of the coefficientwherein the means of determining a watermarked value of the coefficientcomprise: means for selecting a modified value of the coefficient, meansfor determining a symbol index, according to the modified value and afirst predetermined function, means for determining the value of themessage symbol corresponding to the determined symbol index, and meansfor verifying that the value of the message symbol previously determinedcorresponds to the transformation of the modified value by a secondpredetermined function.
 13. An insertion device according to claim 12,wherein the determination means are adapted to select the watermarkedvalue from a range of values determined around the value of thecoefficient according to a psycho-visual model.
 14. An insertion deviceaccording to claim 12, comprising: test means, if the value of thepreviously determined message symbol corresponds to the transformationof the value modified by a second predetermined function, fordetermining whether the number of times the symbol has already beeninserted in a coefficient of the image is the lowest amongst all thesymbols whose index was determined according to the modified value andthe first predetermined function and whose value corresponds to thetransformation of the modified value by the second predeterminedfunction, for the coefficient in question.
 15. An insertion deviceaccording to claim 12, being adapted to carry out the insertion of thebinary symbols on the luminance value of the pixels of the image.
 16. Aninsertion device according to claim 12, wherein said index of the symbolis automatically determined in accordance with the coefficient of theimage.
 17. An insertion device according to claim 12, wherein thedetermination and insertion means are incorporated in: a microprocessor,a read only memory containing a program for processing the data, and arandom access memory containing registers adapted to record variablesmodified during the execution of said program.
 18. Apparatus forprocessing a digital image, comprising the device according to claim 12.19. A device for extracting a message from an image, comprising: meansfor calculating, for each coefficient of the image, a symbol index and abinary value, both according to a value of the coefficient, means fortotaling the number of each of the binary values obtained for each ofthe symbol indexes, and means for allocating to each symbol index thebinary value having the largest total.
 20. An extraction deviceaccording to claim 19, being adapted to determine, for a coefficient ofthe image, the symbol index according to the value of the coefficientand a first predetermined function.
 21. An extraction device accordingto claim 19, being adapted to determine, for a coefficient of the image,the binary value according to the value of the coefficient and a secondpredetermined function.
 22. An extraction device according to claim 19,wherein the calculation, totaling and allocation means are incorporatedin: a microprocessor, a read only memory containing a program forprocessing the data, and a random access memory containing registersadapted to record variables modified during the execution of saidprogram.
 23. A device for extracting a message from an image,comprising: means for calculating, for each coefficient of the image, asymbol index according to a value of the coefficient, means forcalculating first and second values according to the value, for eachcoefficient of the image, means for first totaling of the absolutevalues of the differences between the value of the coefficient and thefirst value, for each symbol index, means for second totaling of theabsolute values of the differences between the value of the coefficientand the second value, for each symbol index, means for allocating toeach symbol index a binary value according to the smallest total amongstthe first and second totals.
 24. An extraction device according to claim23, being adapted to determine, for a coefficient of the image, thesymbol index according to the value of the coefficient and a firstpredetermined function.